Background and Relevant Art
Computers and computing systems have affected nearly every aspect of modern living. Computers are generally involved in work, recreation, healthcare, transportation, entertainment, household management, etc.
Computing systems can be used to model geometric objects. For example, computer system can model planar geometric objects such as lines, circles, polygons, etc.
The buffer of distance d around a geometric object o is the set of all point that are within distance d from o. Namely, the buffer about a geospatial object is the set of all points whose distance from the geospatial object does not exceed some prescribed threshold. Buffer is one of the most fundamental constructions in geospatial computations. For example, it may be used to define the danger zone around the path of a hurricane, or as a query window for selecting all the objects in a database which are in the vicinity of a given object.
Even when o is as simple as a point or a line, an exact representation of the theoretical buffer around it uses circular arcs. For example, around a point, the buffer with a distance d is a circle with a radius d. The buffer with a distance d around a line appears rectangular along the length of the line, but has a half circle with a radius d at each end of the otherwise rectangular shape. FIG. 1 illustrates a number of examples of buffers, including a buffer 102 around a point 104, a buffer 106 around a line 108, and a buffer 110 around an arc 112. In the absence of circular arcs, the buffer is approximated by polygons, and higher accuracy requires a corresponding larger number of vertices. The object models of existing products include circular arcs only in planar geometry. No existing product supports circular arcs on an ellipsoid earth model.
The subject matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one exemplary technology area where some embodiments described herein may be practiced.